I've got a Raspberry Pi with a Raspbian SD card, connected to my Debian laptop via a USB TTY cable. The cable is supplying power to the board; my user is in the dialout group, and can see /dev/ttyUSB0. What application should I use to obtain terminal access to my Pi via this serial port?

Once you have this you should be able to use a terminal emulator like minicom on your Debian laptop to connect to the RPi and you will get a login prompt. Make sure the port speed on the laptop matches the settings on the RPi (115200 in the example above).